Nonlinear water waves are common physical phenomena in the field of coastal and ocean engineering, which plays a critical role in the investigation of hydrodynamics regarding offshore and deep-water structures. In the present study, a three-dimensional (3D) numerical wave flume (NWF) is constructed to simulate the propagation of nonlinear water waves. On the basis of potential flow theory, the second-order Runge-Kutta method (RKM2) combining with a semi-Lagrangian approach is carried out to discretize the temporal variable of the 3D Laplace’s equation. For the spatial variables, the generalized finite difference method (GFDM) is adopted to solve the governing equations for the deformable computational domain at each time step. The upstream condition is considered as a wave-making boundary with imposing horizontal velocity while the downstream condition as a wave-absorbing boundary with a pre-defined sponge layer to deal with the phenomenon of wave reflection. Three numerical examples are investigated and discussed in detail to validate the accuracy and stability of the developed 3D GFDM-based NWF. The results show that the newly-proposed numerical method has good performance in the prediction of the dynamic evolution of nonlinear water waves, and suggests that the novel 3D “RKM2-GFDM” meshless scheme can be employed to further investigate more complicated hydrodynamic problems in practical applications.

非线性水波是沿海和海洋工程领域中常见的物理现象，在研究近海和深水结构的水动力方面起着至关重要的作用。在本研究中，构造了三维（3D）数值波槽（NWF）以模拟非线性水波的传播。基于势流理论，结合二阶拉格朗日方法进行了二阶Runge-Kutta方法（RKM2）离散化3D Laplace方程的时间变量。对于空间变量，采用广义有限差分法（GFDM）在每个时间步求解可变形计算域的控制方程。上游条件被认为是施加水平速度的造波边界，而下游条件被认为是具有预定海绵层以处理波反射现象的吸波边界。对三个数值示例进行了详细研究和讨论，以验证已开发的基于3D GFDM的NWF的准确性和稳定性。结果表明，新提出的数值方法在预测非线性水波的动态演化方面具有良好的性能，表明在实际中可以采用新颖的3D“ RKM2-GFDM”无网格方案进一步研究更复杂的水动力问题。应用程序。对三个数值示例进行了详细研究和讨论，以验证已开发的基于3D GFDM的NWF的准确性和稳定性。结果表明，新提出的数值方法在预测非线性水波的动态演化方面具有良好的性能，表明在实际中可以采用新颖的3D“ RKM2-GFDM”无网格方案进一步研究更复杂的水动力问题。应用程序。对三个数值示例进行了详细研究和讨论，以验证已开发的基于3D GFDM的NWF的准确性和稳定性。结果表明，新提出的数值方法在预测非线性水波的动态演化方面具有良好的性能，表明在实际中可以采用新颖的3D“ RKM2-GFDM”无网格方案进一步研究更复杂的水动力问题。应用程序。